Image Deblurring Without Boundary Condition from Accurate Degradation Model via Sparse Representation

Abstract

Image deblurring, which is inherently an ill-posed problem, is generally solved by assuming boundary condition. However, this assumption results in an inaccurate degradation model, and further causes the undesired artifacts in the restoration image when the boundary condition does not match real boundary well. To address the problem, this paper firstly builds an accurate degradation model without boundary condition, which illustrates the real degradation process. Then this paper introduces an image restoration method based on sparse representation to solve the degradation model and obtain the image together with the boundary values, which sometimes contain some important information. Since the boundary values and the image are viewed as the unknown values, the boundary artifacts in the restoration image can be avoided. Experimental results show that the proposed method can achieve the higher quality restoration image and the additional boundary values from the degradation image caused by the blur and random noise, compared with the Lucy-Richardson algorithm under circular, symmetric, replicate boundary conditions and unknown boundary values.